Precision Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>Violation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo stretchy="false">→</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi mathvariant="normal">Ψ</mml:mi><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>Decays

The time-dependent CP asymmetry in B(s)(0)→J/ψK+K- decays is measured using pp collision data, corresponding to an integrated luminosity of 3.0 fb-1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96,000 B(s)(0)→J/ψK+K- decays, the CP-violating phase ϕs is measured, as well as the decay widths ΓL and ΓH of the light and heavy mass eigenstates of the B(s)(0)-B[over ¯]s0 system. The values obtained are ϕs=-0.058±0.049±0.006 rad, Γs≡(ΓL+ΓH)/2=0.6603±0.0027±0.0015 ps-1, and ΔΓs≡ΓL-ΓH=0.0805±0.0091±0.0032 ps-1, where the first uncertainty is statistical and the second, systematic. These are the most precise single measurements of those quantities to date. A combined analysis with Bs0→J/ψπ+π- decays gives ϕs=-0.010±0.039 rad. All measurements are in agreement with the standard model predictions. For the first time, the phase ϕs is measured independently for each polarization state of the K+K- system and shows no evidence for polarization dependence.